We study the one-dimensional non-Hermitian imaginary potential with a real energy spectrum in the framework of the position-dependent effective mass Dirac equation. The Dirac equation is mapped into the exactly solvable Schrödinger-like equation endowed with position-dependent effective mass that we present a new procedure to solve it. The point canonical transformation in non-relativistic quantum mechanics is applied as an algebraic method to obtain the mass function and then by using the obtained mass function, the imaginary potential can be obtained. The spinor wavefunctions for some of the obtained electrostatic potentials are given in terms of orthogonal polynomials. We also obtain the relativistic bound state spectrum for each case in terms of the bound state spectrum of the solvable potentials.

The supersymmetry in non-relativistic quantum mechanics is applied as an algebraic method to obtain the solutions of the Dirac equation with spherical symmetry electromagnetic potentials. We show that some of the superpotentials related to ground state of the solvable potentials in non-relativistic quantum mechanics can be used for studying of the Dirac equation.

The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrödinger-like equation obtained by Dirac equation with the nonrelativistic solvable models is the most efficient method. By this technique, the exact relativistic solutions of Dirac equation for Hartmann and Ring-Shaped Oscillator Potentials are accessible, when the scalar potential is equal to the vector potential. Using solvable nonrelativistic quantum mechanics systems as a basic model and considering the physical conditions provide the changes in the restrictions of relativistic parameters based on the nonrelativistic definitions of parameters.

We show that the radial Dirac equation with constant electrostatic potential and for a large class of the field potentials which are obtained from the master function formalism can be solved by the Rodrigues representation of the orthogonal polynomials. We also show that the Schrödinger-like differential equation obtained from the Dirac equation satisfies the supersymmetry and shape invariant conditions in non-relativistic quantum mechanics. The relativistic energy spectrum for a given potential function is calculated from its corresponding non-relativistic energy spectrum.

This paper presents a general method to solve non-hermeticity potentials with PT (Parity-Time) symmetry using two first-order operators against η-weak-pseudo-hermiticity having positiondependent effective mass. It futher suggests a way to apply this method to Dirac equation with spinor wave functions and non-hermetic potentials with real energy spectrum considering positiondependent effective mass. To show the utilities this method was apply to some superpotentials such as Eckart, Scarf-II, Rosen-Mörse-II and Pöchl-Teller. Finally, it was shown that the real potentials can be converted to complex potentials with eigenvalues of a class of η-pseudo-hermeticity.